MEMS resonators are being intensively studied in many research groups and some first products have recently been released. This type of device offers a high Q-factor, small size, high level of integration and potentially low cost. These devices are expected to replace bulky quartz crystals in high-precision oscillators and may also be used as RF filters. The oscillators are widely used in time-keeping and frequency reference applications such as RF modules in mobile phones, devices containing blue-tooth modules and other digital and telecommunication devices.
Microelectromechanical systems (MEMS) are the technology of the very small, and merge at the nano-scale into nanoelectromechanical systems (NEMS) and nanotechnology. MEMS are also referred to as micromachines (in Japan), or Micro Systems Technology—MST (in Europe). MEMS are separate and distinct from the hypothetical vision of Molecular nanotechnology or Molecular Electronics. MEMS are made up of components between 1 to 100 μm in size (i.e. 0.001 to 0.1 mm) and MEMS devices generally range in size from a 20 μm to a millimeter. They usually consist of a central unit that processes data, the microprocessor and several components that interact with the outside such as microsensors. At these size scales, the standard constructs of classical physics do not always hold true. Due to MEMS′ large surface area to volume ratio, surface effects such as electrostatics and wetting dominate volume effects such as inertia or thermal mass.
There are several ways to excite and to readout the mechanical vibration of a resonator. In most MEMS resonators, excitation is done by electrostatic actuation and readout is done by capacitive or piezoresistive method. In some cases, the actuation can be done by the piezoelectric or thermal expansion.
A piezoresistive readout principle is e.g. described in US20060114541 A1, “Transducer and electronic device”; WO2007036820 A3, “OSCILLATOR BASED ON PIEZORESISTIVE RESONATORS”; and in J. T. M van Beek et al., “Scalable 1.1 GHz fundamental mode piezo-resistive silicon MEMS resonator”, IEDM, Int. Electron Devices Mtg., 2007, ID81339050 “Cantilever piezoresistive silicon resonator”.
Various patent documents disclose MEMS resonators.
Frame shaped MEMS resonators are described in U.S. Pat. No. 7,205,867 and U.S. Pat. No. 6,985,051, different embodiments such as squares, polygons, and rings are shown in these documents. U.S. Pat. No. 7,205,867 mentions the use of piezoresistive elements as electrodes.
A MEMS resonator is shown in US20070046398 where the resonator is shaped as a filled circle with 2 anchors on opposite sides and 4 electrodes on opposite sides to each other.
U.S. Pat. No. 7,323,952 and US20070070821 show MEMS resonators that are ring shaped with inner and outer surface. In U.S. Pat. No. 7,323,952 is it specifically mentioned that the piezoresistive elements can be used for implementing the resonator according to the invention.
The above disclosures mainly focus on the mechanical construction, such as shape, anchors etc, and mode shapes of the resonators. The driving principle is electrostatic and the sense principle is capacitive.
In the following two main prior-art piezoresistive resonator types are described.
1) Piezoresistive Free-Free Beam Resonator
The layout of the free-free beam resonator is shown in FIG. 1 (also described in the first and third references mentioned above). It consists of a free-free beam structure made of Si, which is free at the two ends and anchored at the middle point. The beam has a slit in the middle to direct the sense current. To actuate the device two electrodes are placed at the two free ends. The electrodes are separated from the vibrating structure by two transduction gaps. During operation a combination of AC and DC voltages is applied to the electrodes to drive the structure into resonance. The vibration mode of the structure is the longitudinal bulk-mode (marked by the double-headed arrows in the figure). To sense the vibration (signal readout) the whole Si structure is doped (either n- or p-type) and during operation a sense current is sent through the beam via the anchors (see the arrows in the figure). Due to the piezoresistive effect, the resistance of the beams is changing with the strain induced in the beam when it is vibrating. This readout principle has been proved by experiments to give a few orders of magnitude higher signal than that of the conventional capacitive readout principle.2) Piezoresistive Dog-Bone ResonatorThis is a variation of the piezoresistive free-free beam resonator. Due to the fact that the transconductance (i.e. the signal) of the device scales with the electrode area (i.e. the height times the length of the electrodes), the free-free beam design is modified into the so-called dog-bone design. The dog-bone design consists of two big heads, connected by two arms. The anchors remain at the middle. There is also a slit in the middle of the arms in order to direct the readout current to the two arms. The area of the electrodes, now being the height times the width of the heads, in this device is many times larger than that of the free-free beam design.
The main advantages of the above resonators are very large piezoresistive signal, scalability to high frequency (especially the free-free beam design), less sensitive to gap width, not sensitive to structure height, and a high quality factor. However, during experimenting with these devices a problem is encountered, namely that at relatively large vibration amplitudes they can easily vibrate in some out-of-plane mode shapes, besides the intended in-plane mode shape. FIG. 3 shows an optical observation of a bird-wing out-of-plane mode-shape of a dog-bone resonator operated at relatively high amplitude. The appearance of the parasitic out-of-plane mode shapes leads to a number of negative consequences:
Energy is shared between the modes, that means less energy is stored in the intended in-plane mode. Consequently the efficiency of the device is reduced.
At large vibration amplitudes the signal is not stable and there exist so-called beating patterns in the signal (see an example in FIG. 4). These phenomena are due to complicated couplings between in-plane and out-of-plane vibration modes. The instability in the signal can occur even at lower actuation force at which the bifurcation appears.
As a result, the usable linear range of a device is reduced. The usable linear range is defined as the maximum actuation force below which a linear and stable signal can still be obtained.
The above resonators, such as piezoresistive free beam/lever/dog-bone resonators, can easily vibrate in out-of-plane mode shapes at relatively large vibration amplitudes. This leads to a number of negative effects, such as reduction of efficiency, instability and nonlinearity.
The present invention is aimed at solving one or more of the above mentioned problems and problems associated with the prior art resonators, without jeopardizing other desired characteristics.